BestTimetoBuyandSellStockIV.java

package leetcode;

/**
 * Project Name : Leetcode
 * Package Name : leetcode
 * File Name : BestTimetoBuyandSellStockIV
 * Creator : Edward
 * Date : Dec, 2017
 * Description : 188. Best Time to Buy and Sell Stock IV
 */
public class BestTimetoBuyandSellStockIV {
    /**
     * Say you have an array for which the ith element is the price of a given stock on day i.

     Design an algorithm to find the maximum profit. You may complete at most k transactions.


     dp[i, j] 当前到达第j天可以最多进行i次交易，最大的利润是多少
     tmpMax means the maximum profit of just doing at most i-1 transactions, using at most first j-1 prices,
     and buying the stock at price[j] - this is used for the next loop.


     time : O(k * n)
     space : O(k * n)

     * @param k
     * @param prices
     * @return
     */
    public int maxProfit(int k, int[] prices) {
        int len = prices.length;
        if (k >= len / 2) return helper(prices);

        int[][] dp = new int[k + 1][len];
        for (int i = 1; i <= k; i++) {
            int tmpMax = -prices[0];
            for (int j = 1; j < len; j++) {
                dp[i][j] = Math.max(dp[i][j - 1], prices[j] + tmpMax);
                tmpMax = Math.max(tmpMax, dp[i - 1][j - 1] - prices[j]);
            }
        }
        return dp[k][len - 1];
    }

    public int helper(int[] prices) {
        int len = prices.length;
        int res = 0;
        for (int i = 1; i < len; i++) {
            if (prices[i] > prices[i - 1]) {
                res += prices[i] - prices[i - 1];
            }
        }
        return res;
    }
}